Can I keep my catch?
Usually yes for table fish like dorado, tuna and snapper. Billfish are released on almost every boat in this bay. Your captain decides what comes home, and their word governs on the day.
Dorado, tuna, snapper and other eating fish generally come back to the dock with you, and the crew will fillet and bag them there. It is one of the better parts of a day out here.
Marlin and sailfish are a different matter. Almost every captain in Puerto Vallarta releases billfish as a matter of course, both because the fishery depends on it and because there are limits on what may be taken. If you have your heart set on keeping a particular fish, raise it with the captain before you book rather than on the water.
The captain is the authority on what can be kept on any given day. Ask them, not the internet.